Solve m^39029/64-369

Question

Simplify the expression

\frac{9029}{64} m^{3} - 369

Evaluate

m^{3} \times \frac{9029}{64} - 369

Solution

\frac{9029}{64} m^{3} - 369

Show Solution

\frac{1}{64} (9029 m^{3} - 23616)

Evaluate

m^{3} \times \frac{9029}{64} - 369

Use the commutative property to reorder the terms

\frac{9029}{64} m^{3} - 369

Solution

\frac{1}{64} (9029 m^{3} - 23616)

Show Solution

m = \frac{4 3 369 \times 902 9 ^{2}}{9029}

Alternative Form

m \approx 1.377809

Evaluate

m^{3} \times \frac{9029}{64} - 369

To find the roots of the expression,set the expression equal to 0

m^{3} \times \frac{9029}{64} - 369 = 0

Use the commutative property to reorder the terms

\frac{9029}{64} m^{3} - 369 = 0

Move the constant to the right-hand side and change its sign

\frac{9029}{64} m^{3} = 0 + 369

Removing 0 doesn't change the value,so remove it from the expression

\frac{9029}{64} m^{3} = 369

Multiply by the reciprocal

\frac{9029}{64} m^{3} \times \frac{64}{9029} = 369 \times \frac{64}{9029}

Multiply

m^{3} = 369 \times \frac{64}{9029}

Multiply

More Steps

Evaluate

369 \times \frac{64}{9029}

Multiply the numbers

\frac{369 \times 64}{9029}

Multiply the numbers

\frac{23616}{9029}

m^{3} = \frac{23616}{9029}

Take the 3 -th root on both sides of the equation

3 m^{3} = 3 \frac{23616}{9029}

Calculate

m = 3 \frac{23616}{9029}

Solution

More Steps

Evaluate

3 \frac{23616}{9029}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{3 23616}{3 9029}

Simplify the radical expression

More Steps

Evaluate

323616

Write the expression as a product where the root of one of the factors can be evaluated

3 64 \times 369

Write the number in exponential form with the base of 4

3 4^{3} \times 369

The root of a product is equal to the product of the roots of each factor

3 4^{3} \times 3369

Reduce the index of the radical and exponent with 3

43369

\frac{4 3 369}{3 9029}

Multiply by the Conjugate

\frac{4 3 369 \times 3 902 9 ^{2}}{3 9029 \times 3 902 9 ^{2}}

The product of roots with the same index is equal to the root of the product

\frac{4 3 369 \times 902 9 ^{2}}{3 9029 \times 3 902 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

39029 \times 3 902 9^{2}

The product of roots with the same index is equal to the root of the product

3 9029 \times 902 9^{2}

Calculate the product

3 902 9^{3}

Reduce the index of the radical and exponent with 3

9029

\frac{4 3 369 \times 902 9 ^{2}}{9029}

m = \frac{4 3 369 \times 902 9 ^{2}}{9029}

Alternative Form

m \approx 1.377809

Show Solution